From the given information provided, the first three common denominators of 7/9 and 2/3 are 9, 18, and 27.
To find the common denominators of 7/9 and 2/3, we need to find the least common multiple (LCM) of their denominators.
The prime factorization of 9 is 3 x 3, and the prime factorization of 3 is 3.
The prime factorization of 2 is 2, and the prime factorization of 3 is 3.
The common factors are 3, so the LCM of 9 and 3 is 9.
Therefore, the common denominator of 7/9 and 2/3 is 9.
To find the next two common denominators, we can continue to find the LCM of the denominators with the added factor of 9.
The prime factorization of 18 (2 x 3 x 3) includes the prime factors of 9, so it is a common denominator.
The prime factorization of 27 (3 x 3 x 3) also includes the prime factors of 9, so it is another common denominator.
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The value where the histogram balances when supported at that point is called ____.
The value where the histogram balances when supported at that point is called the mode of the distribution.
The mode of distribution is the value that appears most frequently in the data set. It is often used as a measure of central tendency, along with the mean and median. The mode is especially useful when dealing with categorical or discrete data, where the possible values are limited and well-defined.
For example, the mode of a list of test scores might be the score that occurs most frequently, indicating the most common level of performance. In a histogram, the mode is the value where the distribution is highest, or where the histogram balances when supported at that point.
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Anyone can help? Please..
The correct option is A: A linear pair is two adjacent, supplementary angles.
Describe Supplementary Angles?Supplementary angles are a pair of angles whose measures add up to 180 degrees. In other words, if we place two angles side by side, and their measures add up to 180 degrees, then they are said to be supplementary.
For example, if we have an angle with a measure of 120 degrees, then its supplementary angle would have a measure of 60 degrees, since 120 + 60 = 180. It's important to note that the two angles in a pair of supplementary angles do not have to be adjacent, meaning they can be located anywhere in a figure, as long as their measures add up to 180 degrees.
Supplementary angles play an important role in geometry and mathematics, especially when it comes to solving problems involving angles. For instance, if we know that two angles are supplementary, and we know the measure of one of the angles, we can easily calculate the measure of the other angle by subtracting the known measure from 180 degrees.
In addition, supplementary angles are often used in real-life situations, such as when designing buildings, bridges, or other structures that require precise measurements of angles. Overall, understanding the concept of supplementary angles is crucial for anyone who wants to study and understand geometry and mathematics.
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how much is 140 lbs in kg
On converting the weight of 140 lbs to Kilogram , we get that 140 lbs is equivalent to 63.49 Kg .
The Conversion Factors is used to convert the weight between pounds and kilograms. that means : To convert 1 pound to kilograms , We multiply the number of pounds by 0.4535 .
In this case , we have to convert 140 pounds to kilograms ;
So , we multiply the given weight in pounds with 0.4535 .
On multiplying ,
We get ;
⇒ 140 pounds = 140 × 0.4535 Kg ;
⇒ 140 pounds = 63.49 Kg .
Therefore , 140 lbs is approximately equal to 63.49 Kg .
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The following table shows different choices for making a shake at a restaurant. DeeDee will randomly select one dairy, one fruit, and one topping choice. What is the probability that DeeDee's shake will be made with yogurt, pineapple, and cherries?
Answer:
1/27
Step-by-step explanation:
Probability of DeeDee choosing Yogurt in diary = 1/3
Probability of DeeDee choosing pineapple as fruit = 1/3
Probability of DeeDee choosing cherries as toppings = 1/3
So the Probability of DeeDee's shake being made with yogurt pineapple and cherries = 1/3×1/3×1/3 = 1/27
Find the slope of the line tangent to the y-intercept of the parabola:y=(x+2)^2−4
The slope of the line tangent to the parabola's y-intercepty = [tex](x+2)^2-4[/tex] is 4.
We must first get the parabola's y-intercept in order to determine the slope of the line tangent to it.
We enter x=0 into the equation to obtain the y-intercept:
[tex]y = (x + 2)^2 - 4[/tex]
[tex]y = (0 + 2)^2 - 4[/tex]
y = 4 - 4
y = 0
Hence, the parabola's y-intercept is (0, 0).
The derivative of the parabola's equation must then be determined.
[tex]y = (x + 2)^2 - 4\\y = x^2 + 4x + 4 - 4\\y = x^2 + 4x[/tex]
dy/dx = 2x + 4
By adding x=0 to the derivative, we can now get the slope of the tangent line to the y-intercept:
dy/dx = 2x + 4
dy/dx = 2(0) + 4
dy/dx = 4
Hence, the slope of the line tangent to the parabola's y-intercepty = [tex](x+2)^2-4[/tex] is 4.
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The Olson family uses up a
1/2
-gallon jug of milk every 3 days. At what rate do they drink milk?
The Olson family drinks milk at a rate of 1/6 gallon per day.
To find the rate at which the Olson family drinks milk, we need to divide the amount of milk they drink by the time it takes them to drink it.
They use up a 1/2-gallon jug every 3 days, so their rate of milk consumption is:
(1/2 gallon) ÷ (3 days) = 1/6 gallon per day
A gallon is a unit of volume measurement commonly used in the United States and some other countries. There are different types of gallons, but the most commonly used ones are:
US liquid gallon (abbreviated as "gal" or "US gal"): This is a unit of volume used for measuring liquid substances. It is defined as exactly 3.785411784 liters or approximately 0.83267418 Imperial gallons.
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The area of the rectangle is 34.56cm squared. The diamtetr is 2.75cm. WHAT is the surface area.
The total surface area of the rectangle is 36.4583125cm squared.
What is area?Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.
The surface area of the rectangle can be calculated by multiplying the length of each side by itself. Since the diameter of the rectangle is 2.75cm, each side of the rectangle would be half of the diameter, or 1.375cm. To calculate the surface area, we must then multiply 1.375cm by 1.375cm, which equals 1.8983125cm squared. When combined with the original area of 34.56cm squared, the total surface area of the rectangle is 36.4583125cm squared.
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If the inflation rate was 3% last year and John's salary grew 4%, how much did the purchasing power of his salary change?
John's purchasing power increased by 0.97%.
What is the inflation?
The definition of inflation in the field of economics is "mean increased money supply, but the general public often refer to a sustained increase in the general price level of goods and services in an economy over a period".
If the inflation rate was 3% and John's salary grew 4%, his salary increased more than the rate of inflation. However, his real increase in purchasing power depends on the difference between his salary growth rate and the inflation rate.
To calculate the change in John's purchasing power, we can use the following formula:
Change in purchasing power = (1 + Salary growth rate) / (1 + Inflation rate) - 1
Plugging in the values, we get:
Change in purchasing power = (1 + 0.04) / (1 + 0.03) - 1
Change in purchasing power = 1.01 / 1.03 - 1
Change in purchasing power = 0.0097 or 0.97%
Hence, John's purchasing power increased by 0.97%.
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Can you help me with this problem quickly? Thank you ✨
Answer:
pair c has the inverse functions
A ball is thrown upwards in the air. The height h(t) in feet, of the ball above ground t seconds after being thrown is determined by the expression h(t)=-16t^2+20t+2.
What is the meaning of 2 in the expression?
Answer:
1. The ball is thrown from a height of 2 ft
Step-by-step explanation:
Since 2 does not have a variable that would be the y-intercept; the y-intercept it where the ball is first getting thrown from.
Solve ( x + 6 ) ^2 = 64
A . X = 8 or x = -8
B . X = 2 or x = -2
C . X = 2 or x = -14
D . X = 4 or x = -16
The required solutions to the equation are x = 2 or x = -14.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Starting with the equation:
(x + 6)² = 64
Taking the square root of both sides, we get:
x + 6 = ±8
Solving for x, we have two cases:
Case 1:
x + 6 = 8
x = 8 - 6
x = 2
Case 2:
x + 6 = -8
x = -8 - 6
x = -14
Therefore, the solutions to the equation are x = 2 or x = -14.
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What is the gradient of the surface?
The gradient of the surface can be described as a vector.
The gradient of a surface, which is a vector, represents the size and direction of the sharpest increase in value at a certain location. The magnitude of this vector, which denotes the direction of the greatest rate of rise of the surface, indicates how steep the rise is. The influence of this gradient is felt along a surface, which is the difference. It stands in for a unit that is level with the ground.
In mathematics, the vector grad f(x,y,z) = (df/dx, df/dy, df/dz) represents the gradient of a three-variable function with scalar values, f(x,y,z). Variables like optimization and electromagnetism employ the gradient of a surface, which is a crucial notion in vector calculus. In particular, the gradient of a surface is frequently used to compute the normal vector to a surface or to identify the direction of the steepest rise or drop in a landscape.
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what is the 58 percentage conversion in decimal ?
The conversion value of the given quantity 58 percentage in decimals is equal to 0.58.
Percentage is that quantity of mathematics which represents the fraction of 100.One percentage converted to decimals is written as :
1 percentage = ( 1 / 100 )
= ( 0.01 )
Now Get the value in decimals for 58 percentage using conversion factor we have ,
= 58 percentage
= ( 58 / 100 )
= ( 0.58 ) in decimal form
Therefore, the value which we get after conversion of percentage to decimals is equal to 58 percentage = 0.58 in decimals.
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David is doodling on a rectangular sheet of paper. Beginning in a corner, David draws a line along the long edge of the paper, a distance of 77 cm. Next, David draws a line along the width of the paper, a distance of 36 cm. Finally David draws a diagonal line straight back to the original corner. At this point, David has drawn a total of ___ cm of lines
David has drawn a total of 177 cm of lines.
According to given conditions :We can use the Pythagorean theorem, which tells us that in a right triangle, the square of the length of the hypotenuse (the diagonal line) is equal to the sum of the squares of the lengths of the other two sides (the lines along the long edge and the width).
In this case, the length of the hypotenuse is the distance from the starting corner to the end of the diagonal line, which we can calculate as follows:
d = √(77² + 36²) ≈ 85.99 cm
Therefore, David has drawn a total of 77 cm + 36 cm + 85.99 cm = 198.99 cm of lines. However, we should subtract the length of the starting corner to the end of the first line, which is 77 cm, since it was counted twice (once as part of the diagonal line and once as part of the line along the long edge).
So, the total length of lines that David has drawn is 77 cm + 36 cm + 85.99 cm - 77 cm = 177 cm.
What is Pythagoras Theorem ?Pythagoras' theorem is a fundamental theorem in mathematics that relates to the sides of a right triangle. It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
This can be expressed as:
a² + b² = c²
where a and b are the lengths of the two legs of the right triangle, and c is the length of the hypotenuse.
Pythagoras' theorem can be used to solve a variety of problems involving right triangles, such as finding the length of a missing side or determining whether a triangle is a right triangle. It is also the basis for the distance formula in two and three-dimensional Euclidean space.
Pythagoras' theorem has applications in many fields, including physics, engineering, and computer graphics, and it is one of the most important and widely used theorems in mathematics.
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Rob has $7,869 in an account that earns 13% interest compounded annually.To the nearest cent, how much will he have in 5 years?
Answer:
$14,498.1
Step-by-step explanation:
To find the amount Rob will have in 5 years with compound interest, we can use the formula:
A = P (1 + r/n)^(nt)
where:
A = the future value of the investment
P = the principal amount invested
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have:
P = $7,869 (the principal amount)
r = 13% or 0.13 (the annual interest rate)
n = 1 (the interest is compounded annually)
t = 5 (the number of years)
Substituting these values into the formula, we get:
A = $7,869 (1 + 0.13/1)^(1*5)
A = $7,869 (1.13)^5
A = $14,964.92
Therefore, to the nearest cent, Rob will have $14,964.92 in 5 years.
Express 4 + ln 2 - ln 4 as a single natural logarithm.a. ln 2b. ln 4 c. ln 64
The single natural logarithm for the expression 4 + ln 2 - ln 4 is ln(2). So, correct option is A.
To express 4 + ln 2 - ln 4 as a single natural logarithm, we can use the properties of logarithms to combine the terms.
First, we can use the rule that ln(a) - ln(b) = ln(a/b) to simplify ln 2 - ln 4:
ln 2 - ln 4 = ln(2/4) = ln(1/2)
Now, we can rewrite the expression as:
4 + ln(1/2)
We can use another logarithmic property, ln(a) + ln(b) = ln(ab), to write this as:
4 + ln(2^(-1))
Simplifying further:
4 - ln(2)
Therefore, 4 + ln 2 - ln 4 can be expressed as a single natural logarithm of:
ln(2^2 / 2) = ln(2)
So, the answer is (a) ln 2.
In general, when simplifying expressions involving logarithms, it's helpful to remember the logarithmic properties and rules, such as the product, quotient, and power rules, as well as the fact that ln(e) = 1. By applying these rules systematically, we can simplify complex expressions into simpler forms that are easier to work with.
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Due nowww please help mee
Answer:
Step-by-step explanation:
I cant see
Based on the results, what is the probability of needing more than 6 rolls to get doubles??
___
The probability of needing more than 6 rolls to get doubles is,
⇒ 3 / 20
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
Each student in Mr. Jones class has two standard number cubes.
Hence, The probability of needing more than 6 rolls to get doubles is,
Total number of cubes = 20
More than 6 rolls = 3
Thus, The probability of needing more than 6 rolls to get doubles is,
⇒ 3 / 20
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Determine the unknown angle measures of △DEF. Round to the nearest degree.
m∠D =
°
m∠F =
°
Answer: we can't help you
Step-by-step explanation:
Sorry but it appears that there is an image that goes with this question but you didnt attach it so we can't answer your question
Rob has $7,869 in an account that earns 13% interest compounded annually.To the nearest cent, how much will he have in 5 years?
Step-by-step explanation:
Principal (P)=$7869
Rate (R)= 13%
Time (T)= 5 years
Compound Interest (CI)=?
We know that,
CI = P { (1+R/100)^T -1}
= $7869 {(1+13/100)^5 -1}
= $7869 {(113/100)^5 -1}
= $7869 {(1.13)^5 -1}
= $7869 {1.84-1}
= $7869 × 0.84
= $6609.96
Compound Amount= CI+p
= $6609.96+7869
= $14478.96
Therefore, he will have $14478.96 after 5 years.
let r be the region bounded by the following curves. find the volume of the solid generated when r is revolved about the y-axis.
The volume of the solid generated when r is revolved about the y-axis is 3.2π.
Volume of Solid:
The volume of a solid is a measure of the space occupied by an object. This article explains how to calculate the volume of solids and the volume of regular and irregular solids.
According to the Question:
We know that:
A ( y ) = π × (f₁ (y)² - f₂ (y)²)
where,
f₁ (y) is the function further away from y axis
f₂ (y) is the function closer to y axis
f₁ (y) = 2
f₂ (y) = 2y²
A ( y ) = π × [2² - (2y)²]
A (y) = π × (4 - 4y²)
A (y) = 4π (1 - y²)
Now,
Computing V (y)
[tex]V =\int\limits^1_0 {A(y)} \, dy[/tex]
[tex]V = 4\pi \int\limits^1_0 {(1-y^2)} \, dx[/tex]
V = 4π (1 - 0.2)
V = 3.2π
Therefore, The volume of the solid generated when r is revolved about the y-axis is 3.2π.
Complete Question:
Let R be the region bounded by the following curves. Use the disk or washer method to find the volume of the solid generated when R is revolved about the y-axis. y= square root of (x/2) , y=0 , x=2
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Solve the system by substitution.
y=-7x-3
5x+4y= -35
Answer: (x,y)=(1,-10)
Step-by-step explanation:
y=-7x-3
5x+4y=-35
substitute the value of y
5x+4(-7x-3)=-35
solve the equation
x=1
substitute the value of x
y=-7 x 1-3
solve the equation
y=-10
A possible solution is
(x,y)=(1,-10)
Check the solution
-10=-7 x 1-3
5 x 1+4 x (-10)=-35
simplify
-10=-10
-35=-35
The ordered pair is a solution
(x,y)=(1,-10)
Which graph shows the solution to the system of linear equations?
y = 2x
y=x-2
The solution to the system of linear equations y = 2x and y = x - 2 is (2, 0).
A 25 foot tall flagpole casts a 42 foot shadow. What is the angle the sun hits the flagpole?
The angle the sun hits the flagpole is approximately 33.69°.
Describe angle.An angle is a geometric shape that is defined as the amount of rotation that occurs between two straight lines or planes. Angles are measured in degrees, with 360° representing a full circle.
We need to apply the inverse tangent function to determine the angle at which the sun strikes the flagpole. We are aware that the triangle's adjacent side is 42 feet long and its opposite side is 25 feet tall (the height of the flagpole) (the length of the shadow). This indicates that the following equation should be used to get the angle:
Angle = arctan(25/42)
Therefore, the angle the sun hits the flagpole is approximately 33.69°.
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A shipment of 8 tons of sugar is separated into containers of equal size. If the shipment fills 3 3/5 containers, how much sugar can one container hold?
THIS IS TIMED HELP ME OUT
Therefore, one container can hold 20/9 tons of sugar.
To simplify this expression, we can convert the mixed number 3 3/5 to an improper fraction:
3 3/5 = (5*3 + 3)/5 = 18/5
So the expression becomes:
8 tons / (18/5) containers
To divide by a fraction, we can multiply by its reciprocal:
8 tons / (18/5) containers = 8 tons * (5/18) containers
Now we can simplify the expression and solve for the amount of sugar in one container:
8 tons * (5/18) containers = 40/18 tons/container = 20/9 tons/container
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What is a factor tree for 46?
Factor trees are a means to represent a number's factors, more precisely, a number's prime factorization. The tree's branches are divided up into components. When the branch's final factor is a prime number, the branch comes to an end and we circle the number because there are now only two factors left: itself and one.
The factor tree for 46 is:
46
/ \
2 23
To create a factor tree for 46, we will first identify two factors of 46 that are as close to each other as possible.
One such pair of factors is 2 and 23.
So we write 46 as:
46
/ \
2 23
Since 23 is a prime number, we cannot break it down any further.
Therefore, the factor tree for 46 is:
46
/ \
2 23
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Here's a factor tree for the number 46 is as follows:
46
/ \
2 23
|
23
To start, factor tree, we divide 46 by the smallest prime number, which is 2. This gives us 23 as a factor. Since 23 is a prime number, we cannot divide it any further, so we stop and write down the prime factors of 46, which are 2 and 23.
Therefore, the prime factorization of 46 is 2 × 23.
Note that the product of the prime factors in the tree (2 and 23) gives the original number (46).
Factor trees are useful for determining a number's prime factorization, which can be useful in a variety of mathematical applications. The prime factorization of a number, for example, can be used to simplify fractions, find common factors, and solve problems involving factors and multiples.
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What is the result 3 x 6 ?
Answer:
Step-by-step explanation:
3*6=18
how to convert 300m to feet?
By knowing the conversion factors, we can easily and accurately convert measurements to any unit we desire. In this case, 300m is equal to 984.252 feet.
Measurement conversions are an important aspect of mathematical calculations. They help us convert units of measurement to another, making it easier to compare and understand quantities. In this case, we will look at how to convert 300m to feet.
To convert 300m to feet, we need to know the conversion factor between the two units of measurement. One meter is equal to 3.28084 feet. Therefore, to convert 300m to feet, we need to multiply 300 by the conversion factor.
300m * 3.28084 = 984.252 feet
Therefore, 300m is equivalent to 984.252 feet.
It's important to note that when converting between units of measurement, it's important to use the correct conversion factor to ensure accurate results. Additionally, being familiar with common conversion factors can save time and make calculations easier.
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what does the percentage of completion method calculate?
The percentage of completion method is a widely used accounting method to recognize revenue and expenses over the life of a long-term project or contract.
It is primarily used in construction, real estate, and other industries that undertake large projects that span over extended periods. The method estimates the percentage of work completed, and then assigns that percentage of revenue and expenses to that period.
Under the percentage of completion method, revenue and expenses are recognized proportionally to the progress of the project, and the calculation is based on the cost incurred to date relative to the total estimated cost of the project.
This method is advantageous because it allows for more accurate financial statements that reflect the actual progress and costs of the project.
Overall, the percentage of completion method provides a more accurate representation of the financial position of long-term projects and contracts, and is therefore an essential tool for companies in industries that undertake such projects.
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9 people on a bus in Seattle and the average of their yearly income is $65,000. At the next stop, the highest paid person on the bus (with an income of $120,000 per year) gets off and Bill Gates gets on. Mr. Gates makes 7.6 Billion dollars a year. What is the new average and median salary of people on the bus?
The new average salary of the people on the bus is $84,44,96,111.11 and the median salary will not change and will remain same.
Given, we know that average salary of the 9 people on the bus is $65,000.
Formula for Average = sum of salary of all people/ the number of people.
Let us say average salary of first 8 people is 'S'. Given, salary of the 9th guy on the bus is $120,000 Now, we can write it like this :
⇒$65,000 = (S + $120,000)/9
⇒585,000 = S + $120,000
⇒S = $465,000
Therefore, average salary of 8 people is $465,000 after the 9th guy gets off. Now Bill Gates enters the bus with a salary of $7,600,000,000. New average salary :
⇒ (S + $7,600,000,000) / 9
⇒$84,44,96,111.11
Median will not change since, The median of a set of numbers is the number in the middle when you list them in order. For example, the median of {1, 3, 6, 9, 13} is 6. If you replace the highest number with a different number, the median will not change. In this example, {1, 3, 6, 9, 100} still has a median of 6.
Therefore, the new average yearly income of the people on the bus along with Bill Gates is $84,44,96,111.1111.
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